Dreibein as prepotential for three-dimensional Yang-Mills theory

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically non-trivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.Comment: 13 pages, improved version, section on Jacobian remove

Sphere-constrained ML detection for frequency-selective channels

The maximum-likelihood (ML) sequence detection problem for channels with memory is investigated. The Viterbi algorithm (VA) provides an exact solution. Its computational complexity is linear in the length of the transmitted sequence, but exponential in the channel memory length. On the other hand, the sphere decoding (SD) algorithm also solves the ML detection problem exactly, and has expected complexity which is a low-degree polynomial (often cubic) in the length of the transmitted sequence over a wide range of signal-to-noise ratios. We combine the sphere-constrained search strategy of SD with the dynamic programming principles of the VA. The resulting algorithm has the worst-case complexity determined by the VA, but often significantly lower expected complexity

Solving large scale linear programming

The interior point method (IPM) is now well established as a competitive technique for solving very large scale linear programming problems. The leading variant of the interior point method is the primal dual - predictor corrector algorithm due to Mehrotra. The main computational steps of this algorithm are the repeated calculation and solution of a large sparse positive definite system of equations. We describe an implementation of the predictor corrector IPM algorithm on MasPar, a massively parallel SIMD computer. At the heart of the implemen-tation is a parallel Cholesky factorization algorithm for sparse matrices. Our implementation uses a new scheme of mapping the matrix onto the processor grid of the MasPar, that results in a more efficient Cholesky factorization than previously suggested schemes. The IPM implementation uses the parallel unit of MasPar to speed up the factorization and other computationally intensive parts of the IPM. An impor-tant part of this implementation is the judicious division of data and computation between the front-end computer, that runs the main IPM algorithm, and the par-allel unit. Performanc

T invariance of Higgs interactions in the standard model

In the standard model, the Cabibbo-Kobayashi-Maskawa matrix, which incorporates the time-reversal violation shown by the charged current weak interactions, originates from the Higgs-quark interactions. The Yukawa interactions of quarks with the physical Higgs particle can contain further complex phase factors, but nevertheless conserve T, as shown by constructing the fermion T transformation and the invariant euclidean fermion measure.Comment: LaTeX, 4 pages; presented at PASCOS'0

Instability in scalar channel of fermion-antifermion scattering amplitude in massless QED_3 and anomalous dimensions of composite operators

Instability in the scalar channel of the fermion-antifermion scattering amplitude in massless QED_3 for number of flavours less than the critical value 128/3\pi^2 is demonstrated. The anomalous dimensions of gauge-invariant composite operators are determined to O(1/N). Exponentiation of the O(1/N) infrared logarithm is explicitly demonstrated by evaluating the contribution of the ladder diagrams.Comment: 10 pages, uses axodraw.sty; minor additions, version to appear in Mod. Phys. Lett.

External leg amputation in conformal invariant three-point function

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A new star-triangle relation, involving two spinors and one vector field, is derived and used for the calculation.Comment: 16 pages; last paragraph added in Sec. 10, presentation improved, to appear in Eur. Phys. J.

Is there still a strong CP problem?

The role of a chiral U(1) phase in the quark mass in QCD is analysed from first principles. In operator formulation, there is a parity symmetry and the phase can be removed by a change in the representation of the Dirac gamma matrices. Moreover, these properties are also realized in a Pauli-Villars regularized version of the theory. In the functional integral scenario, attempts to remove the chiral phase by a chiral transformation are thought to be obstructed by a nontrivial Jacobian arising from the fermion measure and the chiral phase may therefore seem to break parity. But if one starts from the regularized action with the chiral phase also present in the regulator mass term, the Jacobian for a combined chiral rotation of quarks and regulators is seen to be trivial and the phase can be removed by a combined chiral rotation. This amounts to a taming of the strong CP problem.Comment: 6 pages, REVTeX; brief discussion available at http://theory.saha.ernet.in/~mitra/scp.htm